That was the question I was asked three years ago by my former CEO at my interview. My answer is the same now as it was then: Time.
Time is what you need to give your full attention to the current customer. It's what enables an analyst or engineer to work through the issue until both they and the customer are satisfied. Time gives the customer the feeling of care, priority and focus from the service desk.
Time is the key to the team writing up each ticket "correctly" and create complete documentation.
Time means the team can reduce manual steps to create automated solutions.
Time lets the team tie up all those loose ends. All those backlogs improvements and general admin that tends to pile up when everyone is running around doing nothing but ticket. It gives them time to develop the tools
Having Time gives the team the ability to learn new skills and undertake formal training.
Onboarding new team members is both quicker, easier and more comprehensive when the team have enough time to spend with the newbie.
When the team have time to breathe the are less likely to get ill, burn out and leave.
The worst thing is managers who need to see the Support team being busy with ticket. As if tickets are the only thing that the team should ever do. Using tickets as the sole metric for a team is counter productive. There is just so much more to a Support Team than ticket chasing.
Without enough time. Documentation suffers, investigations are rushed, resolutions become quick fixes - those "may the problem go away" actions that don't address the cause. Root cause analysis suffers or just doesn't get done and worse, the team are bogged down in manual jobs because there isn't time to create a better solution. When time is crunched the number of work items pushed to the Development team slows and those that do get created are rushed and risk being incomplete or just poorly written.